The <inline-formula><math display="inline" overflow="scroll"><msub><mi>k</mi><mrow><mn>3</mn></mrow></msub></math></inline-formula> coefficient in nonparaxial λ/NA scaling equations for resolution, depth of focus, and immersion lithography

Abstract

The Rayleigh's equations for resolution and depth of focus(DOF) have been the two pillars of optical lithography, defining the dependency of resolution and DOF to wavelength and to the numerical aperture (NA) of the imaging system. Scaling of resolution and DOF as well as determination of k 1 and k 2 have been depending on these two equations. However, the equation for DOF is a paraxial approximation. Rigorously solving the optical path difference as a function of wavelength and NA produces a DOF depending on the inverse of the square of the numerical half aperture instead of the numerical full aperture. Using this new DOF scaling equation and a new coefficient of DOF k 3 , the previously determined DOF have been shown to be overestimated by 10%-20% at NA of 0.6 and 0.8, respectively. The equation for resolution does not suffer from paraxial approximation but both new equations remove an ambiguity when the refractive index in the imaging medium is larger than unity. Application to immersion lithography using these equations is included.